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- W3046210697 abstract "Radical membership testing, resp. its special case of Hilbert's Nullstellensatz (HN), is a fundamental computational algebra problem. It is NP-hard; and has a famous PSPACE algorithm due to effective Nullstellensatz bounds. We identify a useful case of these problems where practical algorithms, & improved bounds, could be given---When transcendence degree (tr.deg) r of the input polynomials is smaller than the number of variables n. If d is the degree bound on the input polynomials, then we solve radical membership (even if input polynomials are blackboxes) in around dr time. The prior best was > dn time (always, dn ≥ dr). Also, we significantly improve effective Nullstellensatz degree-bound, when r ≪ n." @default.
- W3046210697 created "2020-08-03" @default.
- W3046210697 creator A5084229662 @default.
- W3046210697 creator A5091058113 @default.
- W3046210697 date "2020-07-20" @default.
- W3046210697 modified "2023-10-06" @default.
- W3046210697 title "Special-case algorithms for blackbox radical membership, nullstellensatz and transcendence degree" @default.
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- W3046210697 doi "https://doi.org/10.1145/3373207.3404030" @default.
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